Pick up Final 4-6:30 PM 30-Nov-2006

24 Hour Take-Home, Good Luck!

Background

Linear Dynamical Systems (sometimes also called Linear Operator Theory refers to a mathematical representation of a physical system that can be represented by a set of 1^st order differential equations or 1^st order difference (or recursion) equations for discrete time systems. Generally, these systems can be written in a very simple (and very overloaded form) of:

The study of these linear systems started historically in the 1960's and required a Ph.D. in math as a necessary prerequisite. Most of the applications at the time were to aerospace control problems (such as rocket guidance). Today, these types of systems are studied extensively, and applications range from controls to economics. Frequently, these problems are cast as dual problems: design (where the input vector is altered to reach a desired output) and estimation (where a set a sensor measurements are processed to estimate the state of the system).

Prerequisites

The only prerequisites for this class are exposure to Linear Algebra and Differential Equations (AMS/ENG 27 fulfills these just fine). A class on circuits (EE 70), controls (EE 154/241), signals and systems (EE 103), and/or dynamics (PHYS 5/6) would be useful, but are by no means critical. The only other prerequisites are a willingness to do the work, which will be hard at times.

Acknowledgements

This course is based on the Introduction to Linear Dynamical Systems sequence (EE263 and EE363), offered at Stanford by Professor Stephen Boyd. Lecture notes are taken from his published lecture notes, "EE263: Introduction to Linear Dynamical Systems," Fall 2004.

I would like to acknowledge the tremendous help and generosity of Prof. Stephen Boyd of Stanford University in teaching the subject matter to me, for all of his help with the slides, the homeworks, and the course materials. I would also like to thank Prof. Ed Carryer at Stanford University for pioneering this video capture technology, and helping me to set it up. Without their help and inspiration, this class would not be here.

Index of class resources

General Class Information — class and section times, instructor and TA information

Lecture Video — Video files of the lectures, and download information for the right codec.

Handouts — homework problem sets, homework solutions, other helpful handouts

WebForum - for announcements, general discussion, and help

Handouts

• General Course Information
• Course Flyer
• A Primer on Matrices
• Basic Notation used in CMPE240
• Least Squares and Least Norm in MATLAB
• Laplace Transform Supplementary Material
• Phase Plane mapping software in MATLAB and Java
• Example problems for Lecture 2 (solutions)
• Homework
• Homework Solutions
• Class Presentation Slides

Lecture Videos

The technology to record these videos is supported by a grant from the Center for Teaching Excellence (CTE), and it is an experiment. Feedback as to the utility, and the usability of these videos would be highly appreciated. The basic hardware required is a tablet PC with the Office Tablet PC extensions, and a standard headset to capture the lecturers voice. Additionally, a program called Camtasia is used to capture the entire sequence into a standard movie format that can then be viewed at a later time for review and additional study.

You may view these lectures at any time, but do not distribute them beyond the UCSC environment. These lectures have been created using the Camtasia software, and can be played through the Camtasia player software, downloadable for free from techsmith here, or through the standard windows media player with the techsmith codec. A Mac OSX version of the codec can be found here that allows playback of the files.

 

• Lecture #0, 21-Sept-2006, Introduction to Linear Dynamical Systems.
• Lecture #1, 26-Sept-2006, Linear Functions (part A).
• Lecture #1, 26-Sept-2006, Linear Functions (part B).
• Lecture #2, 28-Sept-2006, Linear Algebra Review
• Lecture #3, 03-Oct-2006, Linear Algebra Review
• Lecture #4, 05-Oct-2006, QR Factorization
• Lecture #5, 10-Oct-2006, Least Squares
• Lecture #6, 11-Oct-2006, Least Squares Applications
• Lecture #7, 12-Oct-2006, Multiple Regressors, Fast RLS Update
• Lecture #8, 19-Oct-2006, Simultaneous Optimization, Pareto Optimality
• Lecture #9, 24-Oct-2006, Autonomous LDS
• Midterm Review, 25-Oct-2006, Midterm Review
• Lecture #10, 26-Oct-2006, LDS Examples
• Lecture #11, 31-Oct-2006, Matrix Exponential
• Lecture #12, 1-Nov-2006, Eigenvalues and Eigenvectors
• Lecture #13, 2-Nov-2006, Left and Right Eigenvectors
• Lecture #14, 9-Nov-2006, Jordan Canonical Form
• Lecture #15, 13-Nov-2006, Cayley-Hamilton
• Lecture #16, 16-Nov-2006, Input and Output
• Lecture #17, 21-Nov-2006, Quadratic Forms
• Lecture #18, 28-Nov-2006, Singular Value Decomposition
• Final Review Session, 29-Nov-2006, Final Review
• Lecture #19, 30-Nov-2006, Controllability, Observability

 

• Office Hours #3, 04-Oct-2006, Office Hours
• Office Hours #3, 04-Oct-2006, Office Hours
• Office Hours #4, 05-Oct-2006, Office Hours
• Office Hours #5, 10-Oct-2006, Office Hours
• Office Hours #6, 11-Oct-2006, Office Hours
• Office Hours #7, 12-Oct-2006, Office Hours
• Office Hours #8, 19-Oct-2006, Office Hours
• Office Hours #8, 24-Oct-2006, Office Hours
• Office Hours #9, 26-Oct-2006, Office Hours
• Office Hours #10, 31-Oct-2006, Office Hours
• Office Hours #11, 02-Nov-2006, Office Hours
• Office Hours #12, 09-Nov-2006, Office Hours
• Office Hours #13, 10-Nov-2006, Office Hours
• Office Hours #14(a), 13-Nov-2006, Office Hours
• Office Hours #14(b), 13-Nov-2006, Office Hours
• Office Hours #15(a), 15-Nov-2006, Office Hours
• Office Hours #15(b), 15-Nov-2006, Office Hours
• Office Hours #15(b), 15-Nov-2006, Office Hours
• Office Hours #16, 16-Nov-2006, Office Hours
• Office Hours #17(a), 21-Nov-2006, Office Hours
• Office Hours #17(b), 21-Nov-2006, Office Hours
• Office Hours #18, 22-Nov-2006, Office Hours
• Office Hours #19, 27-Nov-2006, Office Hours
• Office Hours #20, 28-Nov-2006, Office Hours

Homework

Homeworks are handed out in class, and are due back either in class or in my office, 337B Engineering 2, at 6 PM on the Thursday of the following week. Homeworks will only be accepted at the beginning of class, not at the end of class. Homeworks turned in late will not be accepted unless you have prior permission from the instructor. Cooperation and collaboration on the homeworks is encouraged, but this is NOT licence to copy. The work you turn in should be your own.

1. Homework #1: Introducation to Linear Dynamical Systems, Due 28-Sep-2006
2. Homework #2: Some Simple Design and Estimation, Due 05-Oct-2006
3. Homework #3: QR Factorization and Gram-Schmidt, Due 12-Oct-2006
4. Homework #4: Least Squares and Applications, Due 19-Oct-2006
5. Homework #5: Autonomous LDS and Matrix Exponential, Due 02-Nov-2006
6. Homework #6: Eigenvalues and Eigenvectors, Due 14-Nov-2006
7. Homework #7: Inputs and Outputs, Due 21-Nov-2006
8. Homework #8: SVD in all its glory, Due 28-Nov-2006

 

9. color_perception.m for homework #2.
10. inductor_data.m for homework #3.
11. deconv_data.m for homework #3.
12. deconv_data.m for homework #3.
13. deconv_data.m for homework #3.
14. emissions_data.m: MATLAB file for Homework #4
15. e911_data.m: MATLAB file for Homework #5
16. interconn.m: MATLAB file for Homework #7
17. time_comp_data.m: MATLAB file for Homework #7

 

Exams

• Midterm, Oct. 26-27, 2006, will be a 24 hour take-home exam
• Practice Midterm (Solution), given in Fall 2004 at Stanford
• Practice Final (Solution), given in Fall 2004 at Stanford
• sig_est_data.m: MATLAB file for Practice Midterm
• directed_graph.m: MATLAB file for Practice Midterm
• wc_impact_data.m: MATLAB file for Practice Final

 

Homework Solutions

 

1. Homework #1 Solution Set
2. Homework #2 Solution Set
3. Homework #3 Solution Set
4. Homework #4 Solution Set
5. Homework #5 Solution Set
6. Homework #6 Solution Set
7. Homework #7 Solution Set
8. Homework #8 Solution Set

Class Presentation Slides

The class lectures use the digital ink capabilities of the TabletPC. The ink is saved back into the presentation, and the presentation is saved to the website for convenience. This year we are using Classroom Presenter rather than PowerPoint. It apprears to be far more stable, and has several nice utilities for the TabletPC. The presentation files are in the .CSD format, and you will need to download Presenter to view them. Presenter can be downloaded here (we are using version 2.1).

1. Lecture #0: Introduction to Linear Dynamical Systems
2. Lecture #1: Linear Functions
3. Lecture #1(b): Example Problems
4. Lecture #2: Linear Algebra Review
5. Lecture #3: QR Factorization
6. Lecture #4: Least Squares
7. Lecture #5: Least Squares Applications
8. Lecture #6: Regularized Least Squares
9. Lecture #7: Least Norm
10. Lecture #8: Autonomous LDS
11. Lecture #9: Matrix Exponential
12. Lecture #10: Eigenvectors
13. Lecture #11: Jordan Form
14. Lecture #12: Input Output
15. Lecture #13: Symmetric Matrices
16. Lecture #14: SVD Applications
17. Lecture #15: Controllability
18. Lecture #16: Observability

 

19. Office Hours: 04 October 2006
20. Office Hours: 10 October 2006
21. Office Hours: 19 October 2006
22. Office Hours: 24 October 2006
23. Office Hours: 31 October 2006
24. Office Hours: 02 November 2006
25. Office Hours: 09 November 2006
26. Office Hours: 10 November 2006
27. Office Hours: 13 November 2006
28. Office Hours: 15 November 2006
29. Office Hours: 16 November 2006
30. Office Hours: 21 November 2006
31. Office Hours: 22 November 2006
32. Office Hours: 27 November 2006
33. Office Hours: 28 November 2006
34. Midterm Review: 25 October 2006
35. Final Review: 29 November 2006

General Class Information

Lecture times:

Tuesday-Thursday, 10:00 - 11:45 PM, JBE-156

Class Webforum:

WebForum - for announcements, general discussion, and help

Textbooks: note that these are NOT required, but are excellent references

Linear Algebra and its Applications, 3rd Ed. by Gilbert Strang, Brooks Cole, 1988. ISBN: 0155510053.

Instructor:

Name: Gabriel Hugh Elkaim (elkaim@soe.ucsc.edu)

Phone: 831-459-3054

Office: Engineering 2, 337B

Instructor Office Hours:

Tuesday-Thursday, 2:00 - 4:00 PM, and by appointment

Teaching Assistants:

TBD (unlikely to be any)